Photonic bandgap fibers

ABSTRACT

Included among the many structures described herein are photonic bandgap fibers designed to provide a desired dispersion spectrum. Additionally, designs for achieving wide transmission bands and lower transmission loss are also discussed. For example, in some fiber designs, smaller dimensions of high index material in the cladding and large core size provide small flat dispersion over a wide spectral range. In other examples, the thickness of the high index ring-shaped region closest to the core has sufficiently large dimensions to provide negative dispersion or zero dispersion at a desired wavelength. Additionally, low index cladding features distributed along concentric rings or circles may be used for achieving wide bandgaps.

PRIORITY APPLICATION

This application is a divisional of U.S. patent application Ser. No.11/323,177 entitled “Photonic Bandgap Fibers” filed Dec. 30, 2005, nowU.S. Pat. No. 7,209,619, which claims priority to U.S. ProvisionalPatent Application No. 60/640,345 entitled “Dispersion Control inPhotonic Bandgap Fibers” filed Dec. 30, 2004, both of which areincorporated herein by reference in its entirety.

BACKGROUND

1. Field of the Invention

This invention relates to optical fibers and more particularly tophotonic bandgap fibers.

2. Description of the Related Art

The concept of optical waveguides based on photonic bandgap (PBG) inperiodic optical media was first proposed in a theoretical paper by Yehand Yariv in 1978 (“Theory of Bragg Fibers”, Journal of Optical Societyof America, vol. 68, no. 9, September 1978, pp. 1196-1201). Not until 21years thereafter was the first practical demonstration of an opticalfiber guided by the PBG effect reported in a paper by Cregan et alpublished in Science in September 1999 (R. F. Cregan, B. J. Mangan, J.C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C.Allan: “Single-mode Photonic Bandgap Guidance of Light in Air”, Science,vol. 285, September 1999, pp. 1537-1539). In these first demonstrations,the cladding of the optical fiber was formed by triangular stacking ofsilica capillaries and the core was formed by a central large air hole.The cladding of this fiber was not, in cross-section, a set ofconcentric circles of different mediums as proposed in the original 1978paper by Yeh and Yariv, which is referred to as Bragg fiber. The sameprinciples, however, form the basis of both waveguides. A first Braggfiber demonstration was reported in November 1999 by Fink in a paperpublished in Journal of Lightwaves Technology (Y. Fink, D. J. Ripin, S.Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas: “Guiding OpticalLight in Air Using an All-Dielectric Structure”, Journal of LightwavesTechnology, vol. 17, no. 11, November 1999, pp. 2039-2041).

Since the first demonstration of the photonic bandgap fibers (PBGF) in1999, progress has been swift. Smith et al reported PBGF with loss aslow as 13 dB/km in a paper published in Nature in August 2003 (C. M.Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F.Borrelli, D. C. Allan, and K. W. Koch: “Low-loss Hollow-core Silica/airPhotonic bandgap Fiber”, Nature, vol. 424, August 2004, pp. 657-659). Afurther breakthrough came in a post-deadline paper at the Optical FiberCommunications Conference in February 2004 (B. J. Mangan, L. Farr, A.Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason,S. Coupland, R. Flea, and H. Sabert: “Low Loss (1.7 dB/km) Hollow CorePhotonic Bandgap Fiber”, PDP24, Optical Communications Conference,February 2004). Mangan et al reported a PBGF with loss as low as 1.7dB/km.

This progress has brought the technology closer to real worldapplications. A first area of application is high energy optical pulsepropagation. In general, most of the optical power propagating along theoptical fiber is in the core, which typically comprises a hole in thecenter of the PBGF. Light can effectively propagate in vacuum, air, orinert gas with much lower nonlinear coefficients than solids.Accordingly, such hollow cores are an ideal media to propagate opticalpulses with high peak power. Such pulses may not otherwise be guidedover substantial distances in a conventional optical fiber due to pulsedistortion and/or energy loss from nonlinear processes in the coreglass. A first demonstration of such high peak power pulse propagationwas reported in a paper in Science published in 2003 by Ouzounov et al(D. G. Ouzounov, F. R. Ahmad, A. L. Gaeta, D. Muller, N. Venkataraman,M. Gallagher, C. M. Smith, and K. W. Koch, Science, vol. 301, 2003, pp.1702). Xenon gas was used to fill the core during one of the reportedexperiments. Distortion-free transmission over 100 m with pulseintensities up to 10¹³ W/cm² was achieved.

Accurate dispersion control is useful for optical fibers employed forlong haul transmission and pulse shaping. In the absence ofnonlinearity, dispersion dictates the pulse evolution duringtransmission through the optical fiber. In cases where the pulse shapeis to be preserved, e.g. in telecommunications and delivery of opticalpulses, low dispersion may be desirable. In particular, a flat lowdispersion over a wide bandwidth can be helpful. A notable example iswavelength-division-multiplexing in telecommunication where a constantlow dispersion level over the wavelength can help provide a uniformperformance for all carrier wavelengths. Conversely, in cases where apre-determined level of pulse shaping is desirable, a high level ofdispersion with controllable amount of variation over wavelength may bepreferred instead. A notable example is pulse compression in a highenergy pulse system, where a combination of second and third orderdispersion (β₂ and β₃, where β_(m)=d^(m)β/dω^(m), and, β and ω arepropagation constant and optical frequency) can be used to achieve afair amount of compensation.

What is needed therefore is the ability to design optical fibers havingthe desired dispersion characteristics.

SUMMARY

Included among the many structures described herein are photonic bandgapfibers designed to provide a desired dispersion spectrum. Additionally,designs for achieving wide transmission bands and lower transmissionloss are also discussed.

As described below, for example, dispersion in a PBGF can be tailoredfor specific applications by appropriately designing the layers of thecladding. In some case, for example, the strong interaction of core modewith the innermost layer or layers of the cladding can be used to obtaina range of desirable dispersion spectra in PBGFs. For instance, in somefiber designs, smaller dimensions of high index material in the claddingand large core size provide small flat dispersion over a wide spectralrange. Additionally, low index cladding features distributed alongconcentric rings or circles may be used for achieving wide bandgaps. Awide variety of other designs are also possible.

Techniques for the fabrication of PBGF are also described herein. Anexample fabrication technique includes forming of a preform, which is alarge version of the PBGF that may be scaled up, e.g., by a factor offew tens to few hundreds, and drawing of the preform to reduce it to therequired fiber diameter, typically few tens to few hundreds ofmicrometers. Other methods are described.

A variety of applications of photonic bandgap fibers is also presented.Other applications not discussed herein are possible as well.

One embodiment of the invention, for example, comprises a photonicbandgap fiber for propagating light having a wavelength, λ, comprising acore and a cladding disposed about the core. The cladding comprises afirst plurality of ring-shaped regions defined by high index materialhaving an index of refraction, n_(h), and a second plurality ofring-shaped regions having a low index of refraction, n₁. The firstplurality of high index ring-shaped regions has an average thickness, d,and an average periodicity, Λ, such that the ratio d/Λ is less thanabout 0.3. The cladding has a normalized frequency ν=2πd(n_(h) ²−n₁²)^(1/2)/λ that is less than about π radians and the core has awavelength transmission band larger than about 100 nm.

Another embodiment of the invention also comprises a photonic bandgapfiber for propagating light having a wavelength, λ, comprising a coreand a cladding disposed about the core. The cladding comprises a firstplurality of ring-shaped regions defined by high index material havingan index of refraction, n_(h), and a second plurality of ring-shapedregions having a low index of refraction, n₁. The first plurality ofhigh index ring-shaped regions having an average thickness, d. The highindex ring-shaped region closest to the core forms a core claddingboundary that has an average thickness, δ, so as to provide a normalizedfrequency ν=2πδ(n_(h) ²−n₁ ²)^(1/2)/λ that is less than about 1 radian.

Another embodiment of the invention comprises a photonic bandgap fiberhaving a transmission band comprising a core larger than about 10 μm anda cladding disposed about the core. The cladding comprises a firstplurality of ring-shaped regions defined by high index material havingan index of refraction, n_(h), and a second plurality of ring-shapedregions having a low index of refraction, n₁. The first plurality ofhigh index ring-shaped regions has an average thickness, d, and anaverage periodicity, Λ, such that the ratio d/Λ is less than about 0.2.The fiber has a dispersion between about −50 to 50 ps/nm/km over atleast about 100 nm of the transmission band.

Another embodiment of the invention also comprises a photonic bandgapfiber having a transmission band comprising a core and a claddingdisposed about the core. The cladding comprising a first plurality ofring-shaped regions defined by high index material having an index ofrefraction, n_(h), and a second plurality of ring-shaped regions havinga low index of refraction, n₁. The first plurality of high indexring-shaped regions has an average thickness, d, and an averageperiodicity, Λ, such that the ratio d/Λ is less than about 0.2. The highindex ring-shaped region closest to the core has a thickness, δ, largerthan about 1.1 times the average thickness, d. The fiber has adispersion below about −50 ps/nm/km over at least about 20 nm of thetransmission band.

Another embodiment of the invention comprises a photonic bandgap fiberfor propagating light having a wavelength, λ, comprising a core and acladding disposed about the core. The cladding comprises a firstplurality of ring-shaped regions defined by high index material havingan index of refraction, n_(h), and a second plurality of ring-shapedregions having a low index of refraction, n₁. The high index ring-shapedregion has an average thickness, d, such that the fiber has atransmission loss of less than about 100 dB/km at a wavelengthcorresponding to a normalized frequency ν=2πd(n_(h) ²−n₁ ²)^(1/2)/λbetween about (a) 0.55π to 0.85π, (b) 1.05π to 1.75π, or (c) 2.4π to2.7π.

Another embodiment of the invention comprises a photonic bandgap fiberhaving a transmission band comprising a core and a cladding disposedabout the core. The core comprises a first plurality of ring-shapedregions defined by high index material having an index of refraction,n_(h), and a second plurality of ring-shaped regions having a low indexof refraction, n₁. The first plurality of high index ring-shaped regionshas an average thickness, d, wherein the high index ring-shaped regionclosest to the core has a thickness, δ, between about 0.1 to 5 times themaximum thickness, d, such that the fiber has zero dispersion at atailored wavelength.

Another embodiment of the invention comprises an gas analyzer comprisinga light source, an optical fiber, and at least one optical detector. Theoptical fiber comprises a core and a cladding and is optically coupledto the light source. The optical fiber further comprises one or moreholes in the core or in proximity to the core for receiving the gas. Theat least one optical detector is disposed to receive light from the coreof the fiber that is affected by the gas.

Another embodiment of the invention comprises a method of manufacturinga photonic bandgap fiber. The method comprises arranging a plurality oftubes so as to form a plurality of rings of tubes disposed about acenter and excluding at least three rings of tubes from the center toprovide an open region. The method further comprises stretching thetubes thereby reducing the size of the rings and the open region.

Other embodiments of the invention are also possible.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are cross-sectional views that schematically illustrateexamples of the photonicband gap fibers (PBGFs) having a claddingfabricated from a plurality of hollow tubes with 7 and 19 tubes,respectively, removed to form a core.

FIGS. 2A-2F are cross-sectional views that schematically illustrate PBGFdesigns having cladding formed from hexagonally arranged microstructuresthat achieve wider transmission bandwidth and low transmission loss.

FIG. 3A schematically illustrates a Bragg fiber formed from a pluralityof larger concentric tubes having varying diameters and a plurality ofsmaller tubes used to separate larger concentric tubes.

FIGS. 3B-3D schematically illustrates an apparatus and method forfabricating the PBG fiber by stacking circular concentric tubes withvarying diameters and introducing the smaller capillaries between theconcentric tubes such as shown FIG. 3A.

FIGS. 4A and 4B schematically illustrate performs for forming PBG fiberscomprising concentric circular rings formed from a plurality ofmicrostructures arranged along concentric circular paths.

FIGS. 4C and 4D schematically illustrate apparatus and methods forforming the PBG fibers of FIGS. 4A and 4B.

FIGS. 4E-4G schematically illustrate simulated optical modes in the PBGfibers comprising microstructures arranged in concentric circular pathssimilar to FIGS. 4A and 4B.

FIG. 4H schematically illustrates first and second pluralities ofannular ring-shaped regions of high and low index formed from aplurality of tubes arranged in circular paths fused together.

FIG. 5 is a plot that shows bending loss for a 15 cm bending radius fora glass rod having a refractive of 1.45 disposed in air havingrefractive index of 1.

FIG. 6 schematically illustrates a cross-section of a Bragg fibercomprising a plurality of concentric ring-shaped regions of high and lowindex.

FIGS. 7A and 7B schematically illustrate a HE11 mode resulting fromsimulations of a Bragg fiber such as shown in FIG. 6.

FIG. 8 schematically illustrates cross-section of a chirped Bragg fibercomprising concentric ring-like regions of high and low index havingthicknesses that increase with radial distance from the center.

FIG. 9 is a plot of dispersion and confinement loss versus wavelengthschematically illustrating the effect of core size in a Bragg fiber.

FIG. 10 is a plot of dispersion and confinement loss versus wavelengthschematically illustrating the effect of ratio the average thickness andperiod (d/Λ) of the high index region determined by simulating a Braggfiber.

FIG. 11 is a plot of dispersion and confinement loss versus wavelengthfor a Bragg fiber showing the effect of the ratio of the thickness ofthe first layer of high index material and the period of the high indexlayers.

FIG. 12 is a plot of confinement loss and effective modal index versuscore radius for a Bragg fiber.

FIG. 13 schematically illustrates the calculations for determiningtransmission bands in a Bragg fiber.

FIG. 14 schematically illustrates a comparison of the confinement lossdetermined using the analytic formula and full numerical calculation.

FIG. 15 schematically illustrates the formula for determining minimumtransmission loss in a Bragg fiber.

FIG. 16 is a plot of dispersion and confinement loss versus normalizedfrequency showing the effect of the ratio of the thickness and period(d/Λ) of the high index regions for a Bragg fiber.

FIG. 17 is a plot of dispersion and confinement loss versus normalizedfrequency showing the effect of chirps in a Bragg fiber where only theperiod, Λ, of the high index ring-like regions is varied while thewidth, d, is kept constant.

FIG. 18 a plot of dispersion and confinement loss versus normalizedfrequency showing the effect of different chirps in a Bragg fiber whereboth the average width, d, and period, Λ, are varied.

FIG. 19 is a block diagram schematically illustrating a single spantelecommunication system incorporating a PBGF.

FIG. 20 is a block diagram schematically illustrating a multiple spantelecommunication system incorporating PBGFs.

FIGS. 21A and 21B are block diagrams schematically illustrating fiberchirped pulse amplification systems incorporating PBGFs.

FIG. 22A is a block diagram schematically illustrating a gas detectionsystem based on spectral transmission measurement using a PBGF.

FIGS. 22B and 22C are schematic drawings of a multiplexer and ademultiplex, respectively, for combining and separating the gas and thelight in the gas detection system of FIG. 22A.

FIG. 23A is a schematic illustration of a gas detection system based onbackward Raman scattering in a PBGF.

FIGS. 23B and 23C are schematic drawings of a multiplexer and ademultiplex, respectively, for combining and separating the gas and thelight in the gas detection system of FIG. 23A.

FIG. 24A is a schematic illustration of a gas detection system based onforward Raman scattering in a PBGF.

FIG. 24B is a schematic drawing of a demultiplex for separating the gasand the light in the gas detection system of FIG. 24A.

DETAILED DESCRIPTION OF CERTAIN PREFERRED EMBODIMENTS

A photonic band gap fiber (PBGF) 100 such as shown in FIG. 1A comprisesa core 102 and a cladding 104, wherein the cladding comprising aplurality microstructures 106 arranged along hexagonally-shaped pathwaysabout the core. Such a cladding 104 may, for example, be formed bystacking small thin wall tubes in a triangular pattern. As seen in FIG.1A, this triangular pattern results in a hexagonal arrangement and maybe referred to as hexagonal stacking as well. The core 102 shown in FIG.1A may be fabricated by excluding 7 tubes from the center of thehexagonally-shaped pathways. In FIG. 1B, the core 102 in the PBGF 100 isformed by leaving out 19 tubes. The fiber in FIG. 1B has a much largercore size.

These fibers may be formed by drawing the tubes. Although the cladding104 is created by stacking circular tubes, the final cross-section ofthe fiber 100 typically does not contain circular holes because theinterplay of surface tension and viscous flow during the drawing processdistorts the circular holes. The holes are typically pressurized duringdrawing. This pressure plays a major part in determining the final holegeometry.

The tubes may comprises hollow glass tubes, the glass portion comprisinga relatively high index material in comparison to the hollow portion,which is empty and may be evacuated or filled with gas or air. Afterdrawing, the glass portions fuse together forming a high index matrixhaving hollow regions therein. These hollow regions within the glassmatrix form the microstructures 106 that provide the photonic band gapconfinement of the cladding 104.

These fibers 100 made by removing 7 or 19 tubes from the center of ahexagonal stack, however, have a transmission window of less than 100nm. Yet for many applications, a much wider transmission band is useful.As described herein, a wider transmission band or window can be achievedby reducing the thickness of the high index materials in the cladding.Additionally, transmission loss has a minimum at an optimized thicknessof this high index material in the cladding. Higher leakage loss canresult at very small thickness of the high index cladding material, andthus, the cladding no longer provides good confinement. A greater numberof tubes or resulting microstructures can be removed from the center toprovide for the desired core size. A preform comprising the plurality oftubes with many tubes in the center removed can be drawn down to providea desired core size. The cladding dimension can be substantially reducedwhen drawn down to give a desired core size. According, in variousembodiments, the transmission band is large, while transmission loss mayalso be substantially reduced.

An illustration of the stacked preform is shown in FIG. 2A, comprising acore 202, a cladding 204 formed by stacking tubes 205. A core tube 207is used to form the core 202. In this method, small dimension for thehigh index material is achieved by leaving out much more than 19 tubeswhen forming the core 202 using the triangularly stacked cladding. Thepreform is then drawn to yield a certain core size after drawing. Thecladding dimension is much reduced compared to other designs with asimilar core size.

Apart from confinement loss, an additional loss mechanism in PBGF isfrom the presence of surface modes around the core. Guided core modescan couple power into the surface modes. Part of this coupled power issubsequently lost. The presence of surface modes is a direct consequenceof removing tubes in a regular matrix to form a core. Advantageously,however, the number of surface modes can be reduced by reducing orminimizing the width of the high index material around the core. Invarious preferred embodiments, the width of the core/cladding boundaryis much further reduced than that of the corresponding cladding. Muchstronger coupling exists between the guided core modes and these surfacemodes than that of the guided core modes and the modes supported in thecladding. The width reduction of the core/cladding boundary is providedby the techniques described above for reducting the width of the highindex material in the cladding structure.

Accordingly, some loss in PBG fibers is due to the presence of surfacemodes around the core and cladding interface formed by the high indexmaterial closest to the core. This high index material may comprises alayer, which may be annular or ring-shaped as seen in the cross-sectionsuch as shown in FIG. 2A. This high index material forms a high indexboundary around the hollow core 202 that has a relatively low index. Thehigh index material layer may be formed at least in part by the coretube 205. The surface modes are supported by this high index boundaryaround the core. As described above, these surface modes can act asleakage channels for guided core modes. The core modes can couple powerinto these surface modes and the power is then lost through furthercoupling into cladding modes or more likely radiation modes. One methodof solving this problem is to reduce the width of the high indexboundary around the core. Decreasing the width of the high indexboundary may be accomplished by removing the core tube 205 in FIG. 2A.The improved design is schematically illustrated in FIG. 2B, where thecore tube 205 is removed to reduce the thickness of the high indexboundary around the core 202. The designs in FIGS. 1A and 1B can alsobenefit from removing the core tubes. These resultant designs are shownin FIGS. 2C and 2D. The core/cladding can also be selectively etched.

Additionally, a further step can be taken to eliminate surface modes. Inthis approach, a composite structure 208 is used in place of the tubesclosest to the core 204 as is schematically illustrated in FIG. 2E. Asshown, each of the tubes around the core are replaced with a compositetube. In this case, for example, twelve composite structures are used.An example of the composite tube or structure 208 is shown in FIG. 2F.This composite structure 208 is formed by stacking tubes 210 and thendrawing the tubes down to an appropriate size to incorporate into thefinal preform. For example, large bundle of stacked tubes forming thecomposite structure are the drawn down to the same dimension as thetubes in the perform stack.

Repeated stacking and drawing can be used to further reduce thedimension of the high index material. More of the cladding tubes,especially the ones nearer to the core 202, can be replaced by thecomposite structure 208 to be benefited by the small dimension of thehigh index material. This approach thus can substantially reduce theglass dimension around the core. The general approach illustrated inFIGS. 2A-2F is not limited to triangularly stacked cladding and can bealso be used in other methods of stacking. Other variations are alsopossible.

As used herein in a consistent manner as used by those skilled in theart, PBG fiber is fiber that guides light therein largely by thephotonic bandgap effect. Photonic bandgap effect does not necessarilyrequire a periodic cladding structure and only that there are few guidedmodes supported the cladding such that the guided modes in the core,which is surrounded or partially surrounded by the cladding, have fewpathways to channel power out of the core. The cladding structure incross-section may comprises a two-dimensional periodic structure formedby a triangularly stacked arrangement of tubes that provides forhexagonally shaped rings of microstructures. The cladding structures mayalso comprise concentric circular rings of alternative high and lowindex optical material. In some embodiments, the cladding structurescomprise concentric circular rings with holes disposed in alternatingones of these concentric circles. A common features of these claddingdesigns is the inclusion of at least two optical materials withrelatively high and a low refractive indices. To provide variousadvantages such as described above, in certain preferred embodiments,the physical dimension of the optical material with the high refractiveindex is small enough so it supports few modes. Typical examples ofcladding include cylindrical structures as described by Yeh and Yarivand triangular or hexagonal arrangements of microstructures as describedin by Cregan et al. Additional discussion of photonic bandgap fibers isprovided in U.S. patent application Ser. No. 10/844,943 entitled “LargeCore Holey Fibers” (Attorney Docket No. IMRAA.024A) as well as U.S.patent application Ser. No. 11/134,856 entitled “Single Mode Propagationin Fibers and Rods with Large Leakage Channels” (Attorney Docket No.IMRAA.035A) are also incorporated herein by reference in their entirety.

As described above, to increase transmission bandwidth and reducetransmission loss of a PBGF, the number of modes supported by thecladding may be reduced, as these supported modes can act as leakagechannels to couple out guided modes in the core. An effective way toreduce the number of modes in the cladding is to reduce the width ofhigh index part of the cladding. The high index material in the PBGfibers such as shown in FIGS. 1A and 1B is included in a plurality ofring-shaped regions. In particular, the ring-shaped regions shown inFIGS. 1A and 1B comprise high index material having microstructuresformed by openings disposed in the high index material. Thesering-shaped regions are arranged about the core. Adjacent ring-shapedregions are also interconnected by webs of the high index material. In atriangularly stacked cladding, these rings take the form of hexagonswith increasing size as they are further away from the core. The widthof the high index ring-shaped regions in the cladding plays a role indetermining the number of modes supported in the cladding, not the arearatio of the high index material and the openings therein having a lowrefractive index, which is often referred to as air filling factor. Asdescribed herein, an optimum width of high index part of the claddingexists that provide for reduced or minimum transmission loss. Thedetails of this optimum width are discussed below using a Bragg fiber asexample of a PBG fiber comprising a plurality of concentric ring-shapedregions.

Circular ring-shaped regions offer some performance advantages incomparison to hexagonal ring-shaped regions illustrated in the FIGS. 2Cand 2D. These advantages may include wider transmission bandwidth andlower transmission loss. Details are discussed below in connection withresults of simulations of Bragg fibers. Such a Bragg fiber comprises thehigh and low index materials arranged in alternating concentric ring orring-shaped regions about the core. A Bragg fiber is, however, difficultto implement when using air as the low refractive index material.

FIG. 3A schematically illustrates a Bragg fiber 300 comprising a core302 surrounded by a cladding 304 comprising substantially circularconcentric ring-like regions 306, 308 of high and low index,respectively, wherein the low index region comprises air. The high andlow index regions 306, 308 alternate. Note that these regions 306, 308are circular as seen in the cross-sectional views shown but arecylindrical when considering the longitudinal direction of the fiber300. In particular, large cylindrical tubes of varying diameters areused to form concentric rings 306. Small tubes are used as spacers 310.The core 302 is disposed at the center of the concentric regions 306,308.

The design in FIG. 3A can be stacked using an apparatus 312 such asillustrated FIG. 3B. The apparatus 312 includes a first holder 314comprising elongated slots that hold the small tubes 316. A secondholder 318 comprises series of V-groves that support the large tubes320. The apparatus 312 is further illustrated in FIG. 3C, where theelongate slots and V-grooves are shown. The first holder 314 with smalltubes 330 is further illustrated in FIG. 3D.

Another design having circular stacking is illustrated in FIG. 4A. Acentral opening 402 forms the core. A core tube 403 comprising a largerdiameter tube is used to form the core/cladding boundary. Small tubes406 having smaller diameters are used to form the cladding. In theembodiment shown, each of the smaller tubes 406 have the same diameter.The small tubes 406 are arranged in circular patterns. In a preferredembodiment, the core tube 403 is removed as is illustrated in FIG. 4B.

An apparatus 412 used for stacking this preform is shown in FIG. 4C. Aholder 414 includes openings that hold pins 415, which in turn hold thesmall tubes 406. The holder 414 also includes a central opening 417 forholding the core tube 403. A fully stacked preform 418 is furtherillustrated in FIG. 4D. Although in this example the holder arranged thetubes along concentric circular pathways, the holders can be configuredwith any arbitrary pattern.

Once a stacked perform is formed, two tapers are made a small distanceaway from the holders, for example, by heating the tubes at locations inproximity to the holders to fuse the tubes together at the two ends. Theholders can then be removed. The stack may be inserted into anotherlarger tube and fused over its entire length with a moving burner. Twoends of the stack may be cut open to allow further etching of surfacelayers and deposition of high purity softer glass using, e.g., achemical vapor deposition system. The etching process can help to removesurface contamination. The deposition of a softer glass layer on thesurface layers can help to reduce scattering loss by providing asmoother surface. The perform is subsequently drawn to form fiber.

Simulations have been performed for a fiber 420 shown in FIG. 4E. Asillustrated in FIG. 4E, the fiber 420 comprises a plurality ofmicrostructures 424 arranged in concentric circular patterns. Themicrostructures 424 comprise holes or openings formed in a matrixmaterial 426. The holes or openings are evacuated or filled with air orgas that yields a relatively low refractive index in comparison to thematrix material 426 which may comprises, e.g., glass, and has arelatively high refractive index. The arrangement of microstructures 424in the matrix material 426 creates concentric ring-shaped regions ofhigh index material (the glass) and concentric ring-shaped regions oflow index (the openings). Adjacent ring-shaped regions are connected bywebs 428 of the high index material 426.

Simulated fields of the HE11 mode are shown in FIGS. 4E-4G. FIG. 4Eshows the longitudinal electric field, FIG. 4F shows the longitudinalmagnetic field, and FIG. 4G shows the transverse electric field.

FIG. 4H illustrates an example of a drawn fiber 430 comprising a core432 and a cladding 434. The hole boundaries (sidewalls of the smalltubes 416) are joined to form a first plurality of concentric rings orring-shaped regions 431 having circular cross-sections centered at thecenter of the core 432. These ring-like regions 431 comprise therelatively high index material, e.g., glass. The rings 431 are linkedtogether by webs 433 formed from part of the hole boundaries (e.g.,sidewalls of the small tubes 416). These webs 433 comprise the highindex material as well. The innermost ring-shaped region 431′, the layerclosest to the core 432, is also indicated. The fiber 430 also includesa second plurality of concentric rings or ring-shaped regions 435 havingcircular cross-sections centered at the center of the core 432. Thesecond plurality of ring-shaped regions 435 comprises the circulararrangement of evacuated or gas or air filled openings forming themicrostructures and has a relatively low index. The first and secondring-shaped regions 431, 435 alternate.

To assess the affect of the width of the high index material in thecore/cladding boundary of a PBGF for reducing or minimizing the numberof supported surface modes, simulations are performed. In particular,the mode supported by a high index rod of radius δ and index n_(h)embedded in a low index background of index n₁ is calculated for awavelength λ. In this case, the V value derived for conventional opticalfiber can be used.

$\begin{matrix}{V = {\frac{2{\pi\delta}}{\lambda}\sqrt{n_{h}^{2} - n_{l}^{2}}}} & (1)\end{matrix}$

Only a fundamental mode is supported when V<2.405 and this fundamentalmode will never cut off. At least 2 modes are supported if thefundamental mode is considered to have a two-fold degeneracy. Inpractice, the supported mode can, however, be so weakly guided when V issmall, that the fundamental mode is effectively not supported. To obtainthis practical limit for V, the loss of a bent optical fiber isdetermined using the loss formula given by Snyder and Love in OpticalWaveguide Theory (Chapman and Hall, 1983). If power transmission in anoptical fiber can be expressed as P(z)=P(0)exp(−γz) over a bent fiberhaving a bend radius of R_(c), γ can be obtained in the followingformula for the fundamental mode in a step index fiber.

$\begin{matrix}{\gamma = {\frac{\sqrt{\pi}}{2\delta}\sqrt{\frac{\delta}{R_{c}}}\frac{U^{2}}{V^{2}W^{3/2}{K_{1}(W)}^{2}}\exp\left\{ {{- \frac{4}{3}}\frac{R_{c}}{\delta}\frac{W^{3}\Delta}{V^{2}}} \right\}}} & (2)\end{matrix}$where U and W are as normally defined for a waveguide, K₁ is modifiedBessel function of the 1^(st) order, and Δ=(n_(h)−n₁)/n_(h). For smallV, where V≈U, the bend loss formula can be simplified.

$\begin{matrix}{\gamma = {\frac{\sqrt{\pi}}{2\delta}\sqrt{\frac{\delta}{R_{c}}}\frac{1}{W^{3/2}{K_{1}(W)}^{2}}\exp\left\{ {{- \frac{4}{3}}\frac{R_{c}}{\delta}\frac{W^{3}\Delta}{V^{2}}} \right\}}} & (3)\end{matrix}$

The bend loss is calculated for a glass rod of refractive index of 1.45surrounded by air with a refractive index of 1 for a bending radius of15 cm and shown in FIG. 5. The bending loss is plotted in dB/m for fourwavelengths at 0.5, 1.0, 1.5 and 2 μm. The bending loss exceeds 1000dB/m at around V=0.64-0.66 for all the wavelengths considered.Considering the arbitrariness of the choices of 1000 dB/m and 15 cmbending radius, a V value of 0.5 provides a reasonable practicalguidance for fundamental mode cut off. In this example, using the Vvalue of 0.5, the rod diameter is as small as 76 nm, 152 nm, 227 nm and303 nm for the wavelengths of 0.5 μm, 1.0 μm, 1.5 μm and 2.0 μm. Thesenumbers offer an approximate upper limit for the thickness of the highindex material in the core/cladding boundary of PBGF not to support anymodes in a practical sense. In this case, δ is chosen to be the maximumthickness of the high index core/cladding boundary. In practice, it isnot necessary to go far below this limit, as less benefit is expected interms of eliminating surface modes, while benefit of the first layer'scontribution to confinement loss will be substantially reduced when δ istoo small. The guided mode will also more likely penetrate through thiscore/cladding layer if it is too thin. This can increase scattering lossdue to imperfections in this layer in addition to the increase ofconfinement loss. Although, this analysis is done for n_(h)=1.45 andn₁=1.0, the same analysis can be done for any other two materialcombination. In a cladding with layers of high index materials, themaximum thickness of core/cladding boundary layer may need satisfy theabove limit. This design approach may be used for triangularly stackedcladding where the high index layers are in the form of hexagonssurrounding the core as well as a Bragg fiber. This approach is alsoapplicable to other designs. The range of thickness values, however, isnot limiting as values outside these ranges can be used. Othervariations are also possible.

Bragg fiber formed by alternating glass and air layers have beendiscussed above. The cross-section of a Bragg fiber 600 is shown in FIG.6. This cross-sectional view shows a core 602 and cladding 604. Thecladding 604 comprises a plurality of ring-shaped regions 603, 605 ofalternating high and low refractive index. The ring-shaped regions 603of high index may comprise material having a relatively high index ofrefraction and the ring-shaped regions 605 of low index may comprisematerial having a relatively low refractive index.

Certain parameters are also shown in FIG. 6. A is the period of periodiccladding. d is the thickness of the high refractive index layers (n_(h))603 and D is the thickness of low refractive index layers (n₁) 605. Theindex of the media 609 outside the cladding region 604 is defined as n₀.n₀ has a small imaginary part in the simulations to enable thecalculation of modal confinement loss. N is total number of layers. Whena layer has different properties, a subscript n is used to denote eachparameter. n is between 1 to N. where 1 denotes the innermost layer.Ratio R is defined as d/Λ. Chirp is defined as (Λ_(i-1)−Λ_(i))/Λ_(i),which remains constant for all layers in the simulation of the Braggfiber of FIG. 6. The core 602 has a radius of ρ. The following valuesare used in the simulations if not specifically given: n_(h)=1.45, n₁=1,n₀=1+i1e-8, ρ=5 μm, R=0.1, Λ=3.5 μm, chirp=0 and number of layer N=10.When a chirp is introduced, Λ₁=3.5 μm is used, i.e. the first layer wasnot changed. Despite that the Bragg fiber 600 is used for varioussimulations discussed herein, the general conclusion should apply toother types of PBGFs.

This model is based on boundary field matching with fields decomposed ina Fourier-Bessel series. A simulated HE11 mode in a Bragg fiber isillustrated in FIGS. 7A and 7B. The longitudinal electric field,longitudinal magnetic field and transverse electric field are given inFIG. 7A, while the radial distributions of the E_(z), H_(z), E_(r) andE_(θ) are given in FIG. 7B.

Two types of chirped Bragg fiber are also studied. The first type isillustrated in FIG. 8, where both the period Λ and thickness d of thehigh index layer 603 are changed from layer to layer in a linearfashion. In a second type of chirped structure, only the period Λ ischanged while the thickness d of the high index layer is kept constant(not shown).

The effect of core radius on fiber dispersion is shown in FIG. 9. Fourcore radii, 15 μm, 10 μm, 5 μm, and 4 μm, were studied. Mode confinementloss is shown using dotted lines while dispersion is shown with solidlines. As core size increases, the transmission windows widens anddispersion is generally reduced. A low flat dispersion over a widespectrum can be achieved at large core size. Such a dispersioncharacteristic is suitable for telecommunication where multiplewavelengths are transmitted over a wide wavelength range. The ratio(d/Λ) in this simulation is 0.1.

Effect of ratio, R=d/Λ, is shown in FIG. 10, where five ratios, 0.1,0.2, 0.3, 0.4 and 0.5 were simulated. The most significant effect of anincreasing ratio, R, is narrowing of transmission window. This effect isaccompanied by a strong increase of dispersion, while the dispersionslope is also significantly increased. For a low flat dispersion over awide spectrum range as desired in a telecommunications system, smallratio may therefore be useful. Moreover, by employing a combination ofsmall ratio and large core, a very low flat dispersion profile over awide spectrum range is possible. The core size in this simulation is 5μm. As shown in FIG. 9, dispersion between 0 to 7 ps/nm/km over abandwidth as wide as 1000 nm can be obtained with a ratio of 0.1 and acore size of 15 μm.

In the plots in FIG. 11, only the ratio, R=d/Λ, of the first layer ofhigh index material 603 was changed. In these simulations, the ratio isdetermined using the thickness of the first layer 603 as the value ford. As shown, dispersion and zero dispersion wavelength can be modifiedby adjusting the first layer ratio while the transmission is minimallyimpacted as long the change of the ratio, R, is not too large. In thisexample, first layer ratio may be less than 0.15. FIG. 11 demonstratesthat the zero-dispersion wavelength can be significantly moved towardsthe center of the transmission window by increasing the ratio, R=d/Λ, ofthe first layer 603 (where d is the thickness of this first layer). Thisresult is significant as the high negative dispersion part of thespectrum can thus be used without causing significant transmission loss.

As the curves can be shifted in wavelength by proportionally scaling Λ,any desired part of the dispersion curve can be used by shifting it to aspecific wavelength of interest. Dispersion tailoring can be done forany wavelength this manner. Although the effect of the ratio and coresize are studied, the refractive index of the first layer 603 can alsobe similarly adjusted to obtain the desired dispersion in a PBGF.

FIG. 12 illustrates the number of modes supported in a Bragg fiber forvarious core radii by calculating the confinement loss as well as theeffective indexes of various modes. As shown, low transmission loss canbe realized for all the modes simulated when the core radius larger than10 μm. At core radius between 4 μm and 5 μm, only HE11 mode is wellsupported. Below a core radius of 4 μm, all modes have high loss. Thisdata indicates an optimum core size for single mode operation.

Before proceeding to the following analysis, additional definition ofparameters is given below.

-   n_(r): real part of effective index-   n_(i): imaginary part of effective index-   λ: optical wavelength-   ν: normalized frequency-   k: =2π/λ, vacuum wave number-   β: =β_(r)+iβ_(i)=2π(n_(r)+in_(i))/λ, propagation constant-   α: =2πin_(i)/λ, confinement loss-   k_(h): =k(n_(h) ²−n_(r) ²)^(1/2), transverse wave vector in the high    index media-   k₁: =k(n_(r) ²−n₁ ²)^(1/2), transverse wave vector in the low index    media-   m: order of transmission or stop bands, m∈(1, ∞)

In certain preferred embodiments of PBGF, the effective index n_(r) ofthe guided mode is very close to the core refractive index n₁. Thisapproximation leads to k₁≈0 and k_(h)=k(n_(h) ²−n₁ ²)^(1/2). In thelimit of n_(r)≈n₁, for TE-like modes,

$\begin{matrix}{{\mathbb{e}}^{{\mathbb{i}}\; k_{TE}\Lambda} = {{\cos\left( {k_{h}d} \right)} - {{\frac{k_{h}D}{2}{\sin\left( {k_{h}d} \right)}} \pm \sqrt{\left\lbrack {{\cos\left( {k_{h}d} \right)} - {\frac{k_{h}D}{2}{\sin\left( {k_{h}d} \right)}}} \right\rbrack^{2} - 1}}}} & (4)\end{matrix}$

The amplitude of the exp(ik_(TE)Λ) determines the convergence ordivergence of the modal field, the bandgap of the Bragg fiber aredetermined as:|e ^(ik) ^(TE) ^(Λ)|<1 transmission bands of the fiber|e ^(ik) ^(TE) ^(Λ)|≧1 stop bands of the fiber   (5)

Since the amplitude of the exp(ik_(TE)Λ) provides a measurement of thedegree of all TE-like mode confinement, this amplitude is proportionalto the modal confinement loss. The transmission band boundary isdetermined by |exp(ik_(TE)Λ)|=1. If a normalized frequency is define asν=kd(n_(h) ²−n₁ ²)^(1/2) and in the limit of n_(r)≈n₁, ν=k_(h)d, thenthe upper limits of the transmission band are determined by ν_(h)=mπ,where m determines the order of the transmission band and is integer.Lower limits of the transmission bands (lower frequency limit) ν₁ aredetermined by the following equation:

$\begin{matrix}{{v\;{\tan(v)}} = \frac{2R}{1 - R}} & (6)\end{matrix}$

FIG. 13 plots the tan(ν) and 2R/(1−R) at various values. Theintersection points determine lower transmission limits. Multipletransmission bands are consequence of the periodic nature of tan(ν).

The upper transmission limits are independent of waveguide parametersand lower transmission limits depend only on R. As illustrated, thenormalized frequency ν is only dependent on the dimensional parameter dand becomes independent of period, Λ. Accordingly, the period Λ does notplay a role in determining the limits of the transmission bands. Therelationship for determining the lower limit of the transmission band isshown in FIG. 13. The ratio R plays a minor role in determining thelower limits of the transmission bands. Many transmission bands arespaced apart in normalized frequency ν by π. Furthermore, the lowertransmission band limit increases with R. The transmission band getsnarrower as the width of the low index layers get narrower.

The precise amount of confinement loss is determined by the modal fielddistribution, which is also influenced by the core design.|exp(ik_(TE)Λ)| is proportional to the confinement loss and is plottedin FIG. 14 against the normalized frequency ν for five different Rvalues. Three transmission bands are shown. As illustrated, the uppertransmission limits are independent of R, while the lower limits of thetransmission bands are related to R. Smaller R leads to widertransmission bands and lower confinement loss. High order transmissionbands have lower confinement loss.

The numerical simulations for R=0.4 and 0.5, are shown in FIG. 14 in bydots. As shown, the numerically calculated confinement loss fits wellwith the simple formulation presented herein with some adjustment ofscale factor. The full numerical results are shown in FIG. 16 for allthe R values plotted against the normalized frequency ν. As shown, theconfinement loss calculated by the numerical model is also consistentwith the formulation described herein.

FIG. 15 plots tan(ν)/ν and (R−1)/(R+1) at various values. Theintersection points determine minimum transmission. The transmissionminimums in FIG. 15 happen at ν_(opt), which is determined by:

$\begin{matrix}{{v\;{\tan(v)}} = \frac{R - 1}{R + 1}} & (7)\end{matrix}$

Two sides of above equation are plotted in FIG. 15. (R−1)/(R+1) isplotted for various R values. The intersection determines the minimumtransmission points, which dependent on R. The transmission minimummoves towards high ν with an increase of R.

Since the simple method of determining transmission bands is based onTE-like modes, this method applies to all the TE and HE modes. Theequivalent formulae for TM and HM modes are:

$\begin{matrix}{{\mathbb{e}}^{{\mathbb{i}}\; k_{TM}\Lambda} = {{\cos\left( {k_{h}d} \right)} - {{\frac{n_{l}^{2}k_{h}D}{2n_{h}^{2}}{\sin\left( {k_{h}d} \right)}} \pm \sqrt{\left\lbrack {{\cos\left( {k_{h\;}d} \right)} - {\frac{n_{l}^{2}k_{h}D}{2n_{h}^{2}}{\sin\left( {k_{h}d} \right)}}} \right\rbrack^{2} - 1}}}} & (8)\end{matrix}$

The uppers limit of the transmission bands are given by ν_(h)=mπ whilethe lower limit of the transmission band is determined by

$\begin{matrix}{{v\;{\tan(v)}} = {\frac{n_{h}^{2}}{n_{l}^{2}}\frac{2R}{1 - R}}} & (9)\end{matrix}$

Full numerical simulation was performed for cases where d is keptconstant while Λ is changed in an incremental fashion from the innermostlayer. The results are shown in FIG. 17 for the first transmission band.With below 2% change in period per layer, the transmission bands aresubstantially unchanged. Above 3% change in period per layer, thetransmission band getters shallower and narrower. This transmission bandreduction and transmission loss increase is due to the outer layers nolonger providing good confinement in phase with the inner layers. Thiseffect is the result of the assumption that n_(r)≈n₁ in derivingequations 6 & 7. This assumption makes k₁=0 and D irrelevant. Inpractice, n_(r) is close to but not equal to n₁, so that the Bragg fibercharacteristics have a weak D dependence. As demonstrated in FIG. 17,large variation of D will reduce transmission bandwidth and increasetransmission loss.

Note that with a 3% change in period per layer, the period of theoutmost layer is 30% larger than that of the innermost layer.

Another simulation was run for the same fiber with various chirps, i.e.both d and Λ are changed incrementally form innermost layer. The resultsare shown in FIG. 18. Even at 1% of chirp, the upper transmission limitis significantly changed. At 2% chirp, the transmission band issubstantially weakened and narrowed.

Based on these results, both d and D are kept constant from layer tolayer in various preferred embodiments, so as to provide increased ormaximum transmission bandwidth and reduced or minimum transmission loss.Using a constant value of d appears to have a stronger effect than usinga constant value of D. For the same reason, a constant d and D aroundeach circumference is also use in certain embodiments. For example, in atriangularly stacked claddings, variation of both d and D around eachlayer surrounding the core can lead to a reduction of overalltransmission bandwidth and an increase of transmission loss comparingwith a Bragg fiber. In certain embodiments, however, d and/or D arevaried.

FIGS. 17 and 18 show that the outer cladding layers have less influenceon dispersion properties. The most significant impact of the chirp isreduction of transmission window. Dispersion is changed little in fiberswhere the inner most layer is identical.

In these simulations of Bragg fibers, the impact of surface modes, whichwill further reduce the transmission bandwidth, has been ignored. Asdiscussed above, in a design that excludes surface modes, V=2πδ*(n_(h)²−n₁ ²)^(1/2)/λ<0.5, where δ is the maximum thickness of thecore/cladding layer. FIG. 14 shows that a small R allows a widetransmission bandwidth. The widest possible transmission bandwidth inwavelength domain is when ν is from ν₁ to ν_(h)=π, i.e. λ fromλ_(min)=2d(n_(h) ²−n₁ ²)^(1/2) to λ_(max)=2πd(n_(h) ²−n₁ ²)^(1/2)/ν₁,where ν₁ depends on R and is given by equation 6. The upper wavelengthlimit λ_(max) is a result of loss of confinement when ν is too small.The lower wavelength limit λ_(min) is a result of the existence oftunneling process in the cladding. A smaller d would give a lowertransmission band limit λ_(min).

The lowest loss can be achieved in the absence of surface modes whenoperating at the highest possible m and at ν=ν_(opt). However there willbe more surface modes at higher m. This fact typically limits thehighest possible m to operate. A smaller core/cladding thickness δ willallow operation at higher m without the penalty of the surface modes,hence lower possible transmission loss. Note, however, that thetransmission band gets narrower in the wavelength domain as m increases.

The results of FIG. 14 pertain to a Bragg fiber where there is uniform dand D circumferentially. In a general situation where d is not uniform,e.g. in the case of triangularly stacked cladding, the minimum loss willno longer occur at ν=ν_(opt) as determined by equation 7 and the shapeof the transmission band in FIG. 14 will no longer apply. Nevertheless,the effect can be studied by considering the effect of a summation overa range d and D. The effective maximum transmission band will narrow andminimum transmission loss will increase, but there will still be alowest loss at a new optimum ν=ν_(opt). It is therefore better incertain embodiments to use a cladding geometry having a substantiallyuniform d and D.

The cylindrically stacked cladding designs illustrated in FIGS. 4A and4B are similar to the Bragg fiber illustrated in FIG. 3A and FIG. 6 whendrawn into optical fibers. The holes will be slightly pressurized duringfiber drawing. This will lead to a disappearance of the gaps betweentubes in FIG. 4A. As discussed above, FIG. 4G illustrates an example ofsuch a drawn fiber. The hole boundaries will be joined to formconcentric circular layers 431 centered about the center of thestructure. The circular layers or rings 431 will be linked between themby webs 433 formed from part of the hole boundaries. The fiber 430 alsoincludes concentric rings 435 comprising the circular arrangement ofevacuated or gas or air filled openings.

Accordingly, the PBG fibers formed from microstructures arranged in acircular pattern are similar to a Bragg fiber. Both comprisesubstantially ring-shaped regions of high and low refractive index.These substantially ring-shaped regions of high and low refractive indexare concentric and are centered about the core. These substantiallyring-shaped regions of high and low refractive index alternate.

In the case where the PBG fiber comprise cladding formed by a pluralityof microstructures such as shown in FIGS. 4E and 4F, the averagethickness, d, of the high index regions may be calculated betweencenterlines through the low index regions. These centerlines passthrough the centers of the microstructures forming the low index region.In the case where the low index regions are circular or annular, thesecenterlines will also be circular or annular as the microstructures arearranged along circular or annular paths. Example centerlines A, B areshown in FIG. 4F. In general, the spacing between the two centerlinescorresponds to the pitch, Λ.

The average thickness of the high index material between these twocenterlines A, B may be computed in different ways. One method ofdetermining this average thickness is to calculate the area of the highindex material located within these two centerlines A, B. This area canbe uniformly distributed along an annular pathway that extends aroundthe core between and equidistant to the two circular or annularcenterlines. The width of this annular pathway between the twocenterlines corresponds to the average thickness of the high indexmaterial, d. This average thickness is computed for the other rings ofhigh index material in a similar fashion to obtain a thickness, d, thatan average across the cladding. Other ways of calculating the averagethickness of the high index material between the two centerlines mayalso be used.

The same approach for determining the average thickness of the highindex material is applicable ring-shaped regions of high index havingother shapes as well. In the case, for example, where themicrostructures are arranged to form hexagonal rings, the centerlinesare hexagonal as the centerlines pass through the centers of themicrostructures forming the ring. The thickness of the high indexmaterial between these hexagonal centerlines may be determined to obtainthe value, d. The same approach can be used for any arbitrary shapedregions of high index material and is not limited to circular orhexagonal shapes.

A similar approach can be used to determine the average thickness, δ, ofthe innermost high index region closest to the core. The averagethickness of the high index material within the centerline through thering of microstructures closest to the core is determined. In FIG. 4F,for example, centerline A is used. In one method, the area of all thehigh index material within this first centerline, A, is computed anduniformly distributed along an annular pathway adjacent to and boundedby the first centerline. Accordingly, the outermost border of thisannular pathway will generally pass through the center of themicrostructures in the first ring. The thickness of this annular pathwaycorresponds to the average thickness, δ. As discussed above, the averagethickness of hexagonal or other shaped rings may be computed in thismanner as well. One skilled in the art will know how to determine theaverage thicknesses, d and δ, of the high index material based on thedescription provided herein.

The low transmission loss and low dispersion over a wide wavelengthregion of several hundred nanometers as illustrated in FIG. 9 is veryuseful for wavelength-division-multiplexing systems fortelecommunications, where tens to hundreds of channels, each at adifferent wavelength, can be sent over a single optical fiber. Inaddition, such systems also have a much reduced nonlinearity due to mostof the guided light being in gas or vacuum. This feature allows higherpower to be launched and consequently higher transmission rate and/orlonger transmission distance without amplification.

FIG. 19 illustrates such a telecommunication system incorporating a PBGF1905. Signals from transmitters 1901 are multiplexed by a multiplexer1902 and are then pre-compensated by a dispersion pre-compensation unit1903 and amplified by an amplifier 1904. A single span of PBGF 1905 isused for transmitting the signals over a distance from source todestination. The transmitted signals are then amplified at thedestination by an amplifier 1906. A dispersion compensation unit 1907 isused before the de-multiplexer 1908. Each signal is finely compensatedby post-compensation unit 1909 to take out any channel dependenttransmission distortion before receipt by a plurality of receivers 1910.FIG. 20 illustrates a similar transmission system that also includestransmitters 2001, a multiplexer 2002, a pre-compensation unit 2003 andan amplifier on the source end and a demultiplexer 2012, a plurality ofpost-compensation units 2013 and receivers 2014 on the destination end.In the system shown in FIG. 20, however, multiple spans of PBGF 2005,2007, 2009 are included. Additional dispersion compensation units andamplifiers 2006, 2008, and 2010 in each span are also included. Opticalconnection is provided between the optical components as shown in FIGS.19 and 20, although structures may be included between these opticalcomponents as well. A variety of these components may comprise opticalfiber. FIGS. 19 and 20 only show the key components of atelecommunication system. Additional components can be added. Likewise,some components in FIGS. 19 and 20 can be omitted and/or locationschanged in different embodiments. Other configurations and variationsare also possible.

PBGF can also be employed in systems for generating optical pulses suchas ultrafast optical pulses. Additional details regarding ultrafastpulse systems is included in U.S. patent application Ser. No. 10/814,502entitled “Pulsed Laser Sources” (Attorney Docket No. IMRAA.023A) andU.S. patent application Ser. No. 10/814,319 entitled “High Power ShortPulse Fiber Laser” (Attorney Docket No. IMRAA.025A), which areincorporated herein by reference in their entirety.

FIG. 21A, for example, illustrates a fiber chirped pulse amplification(FCPA) system incorporating a dispersion tailored PBGF 2106. Pulses fromoscillator 2101 are pre-chirped by using a pre-chirp unit 2102 and arethen amplified by a pre-amplifier 2103. Pulse picker 2104 can be used topick a subset of pulses, which are then amplified by main amplifier2105. The PBGF 2106 is used to compress the amplified pulses, which aresubsequently delivered by a low dispersion PBGF delivery fiber 2107.Optical connection is provided between the optical components as shownin FIG. 21A although structures may be included between these opticalcomponents as well. A variety of these components may comprise opticalfiber or optical fiber devices. In FIG. 21B, also shows a fiber pulseamplification system comprising an oscillator 2110, a pre-chirp unit2111, a preamplifier 2112, a pulse picker 2113, a main amplifier 2114.In FIG. 21B, however, the PBGF compressor and delivery fiber arecombined into a single fiber 2115. FIGS. 21A and 21B only show the keycomponents of a pulse amplification system. Additional components can beadded. Likewise, some components in FIGS. 21A and 21B can be omittedand/or locations changed in different embodiments. Other configurationsand variations are also possible.

A PBGF with low loss and a wide transmission band can also be used fortrace gas analysis with much improved sensitivity due to the longinteraction length. FIG. 22A illustrates such a system that detects,identifies, quantifies, or otherwise performs measurements on gasesbased on spectral absorption. A tunable source 2201 is optically coupledto a PBGF 2204 through a multiplexer 2202, which allows gas to beinjected into the core of the PBGF 2204. A gas filter 2203 may beemployed to take out solid particles in the gas stream. At the outputend, a de-multiplexer 2205 is used to separate gas and the optical beam.The optical beam is then directed to a detector 2207. Gas pumps can beconnected to gas filter 2203 and/or gas outlet 2206 to speed up gasflow.

FIG. 22B illustrates a configuration of the multiplexer 2202 comprisinga sealed chamber 2215. Source light propagated by a fiber 2210 iscollimated by a collimating lens 2212 and focused by lens 2213 into aninput end 2211 of the PBGF 2204. Gas is input in through a gas input2214 which may comprise a filter as described above. The de-multiplexer2205 is illustrated in FIG. 22C. The de-multiplexer also comprises achamber 2218, an output end 2220 of the PBG fiber 2204 as well as acollimating lens 2222 and a focusing lens 2223 which receives the lightoutput from the output 2220 of the PBGF 2204 and couples the light intoan output fiber 2221. The demultiplexer 2205 further comprises a gasoutput port 2224. A broad band source and a monochromator can be usedinstead of the tunable light source 2201 in FIG. 22A.

In such a system gas is introduced into the multiplexer and enters intoportions of the PBGF though holes or openings therein. In variouspreferred embodiments, the core is hollow and the gas enters the hollowcore. The gas affects the propagation of the light, for example, byattenuating the light due to absorption at one or more wavelengths. Theabsorption spectrum of the gas can, therefore, be measured using thedetector 2308 and monochrometer or tunable filter 2307. In certainembodiments such as shown in FIGS. 22A-22C the gas is flowed through thePBGF 2204. In such cases, the long length of the fiber 2204 may increasethe interaction of the gas with the light and provide a higher signal.In other embodiments, other properties of the light may be measured.

FIG. 23A, for example, illustrates a trace gas detection system based ondetection of Raman scattered light. The gas is introduced into the fiberand causes Raman scattering which is measured. The gas may enteropenings in the fiber and may, in certain preferred embodiments, flowthrough the hollow core of the PBGF. As described above, the longinteraction length of the PBGF provides increased detection sensitivity.An additional advantage is that a large part of the Raman-scatteredlight is collected and can also propagate within the photonic bandgapfiber. This feature is especially true for PBGF with a wide transmissionband, i.e. larger solid collection angle.

In the embodiment shown in FIG. 23A, a Raman pump 2301 is opticallycoupled through a multiplexer 2302 to a PBGF 2304. An output end of thePBGF 2304 is optically coupled to a de-multiplexer unit 2305. Gas entersthrough a filter 2303 that removes solid particles. Gas exits throughthe outlet 2306 on the de-multiplexer. Pumps can be used at the inlet2303 and the outlet 2306 to speed up gas flow. Back-propagatingscattered light by Raman scattering is directed towards a tunable filteror a monochromator 2307 and onto the detector 2308. The tunable filteror monochomator 2307 and detector 2308 can measure the wavelengthspectrum of the scattered light.

The multiplexer 2302 comprising a sealed chamber 2310A is illustrated inFIG. 23B. Pump light is carried in by an optical fiber 2310 opticallycoupled to the pump source 2301 and is then collimated by a collimatinglens 2313. The collimated pump beam 2318 is focused by a focusing lens2314 into an input end 2311 of the PBGF 2304. A back-propagatingscattered Raman signal 2319 is reflected by a filter 2316, which isdesigned to only reflect Raman signal but not the pump light. The Ramansignal 2319 is focused by a focusing lens 2315 onto an output fiber 2317optically connected to the tunable filter or monochromator. Gas entersin through an gas inlet port 2312 which may comprise a filter.

The de-multiplexer 2305 is illustrated in FIG. 23C. The de-multiplexer2305 comprises a sealed chamber 2325 and a collection lens 2322 thatcollect pump light from an end 2320 of the PBGF 2304. The de-multiplexerfurther comprises a detector 2324 for monitoring the pump light thatpropagates through the PBGF 2304. The collection lens 2322 couple thepump light from the end 2320 of the PBGF 2304 and directs the pump lightonto the detector 2324.

FIG. 24A shows a Raman detection system based on detection of a forwardpropagating Raman signal. In certain preferred embodiments, operation isin the stimulated Raman regime, where much stronger signal is expecteddue to amplification in the presence of high pump power. Theconfiguration shown in FIG. 23A can also be used in a stimulated Ramanmode to detect stimulate Raman emission.

The Raman detection system shown in FIG. 24A comprises a Raman pump2400, a demultiplexer 2402 having a gas input port 2401, a PBG fiber2403, and a demultiplexer 2404 having a gas output port 2405. The systemfurther includes a tunable filter or monochromator 2406 opticallycoupled to the demultiplexor 2404 so as to receive the Raman signaltherefrom. A detector 2407 is also included to sense the Raman signal.

The de-multiplexer 2404 is illustrated in FIG. 24B. The demultiplexer2404 comprises a sealed chamber 2418 that contains the gas. Pump andRaman signals are introduced into the chamber 2418 by an output end 2410of the PGB fiber 2403. The pump and Raman signals are collimated by acollimating lens 2413. The Raman signal 2419 passes through filter 2415,which is designed to reflect the pump light. This Raman signal 2419 isfocused by a lens 2414 onto the fiber 2411 that directs the light to thetunable filter or monochromator 2406. The pump light 2417 is reflectedby the filter 2415 onto a detector 2416 for power monitoring. Themultiplexer 2420 is similar to that shown in FIG. 22B.

Optical connection is provided between the optical components as shownin FIGS. 22A, 23A, and 24A although structures may be included betweenthese optical components as well. A variety of these components maycomprise optical fiber or optical fiber devices.

The systems and components shown in FIGS. 22A-22C, 23A-22C, and 24A-24Bare examples only. One skilled in the art may devise alternativeconfigurations and designs. For example, the filter 2316 shown in FIG.23B can be designed to reflect the pump light and pass the signal. Thefiber positions may be different in such an embodiment. Similarly, thefilter 2415 in FIG. 24B can be designed to reflect the Raman signal.Fiber positions may likewise be different. The pump monitoring functionsin FIGS. 23C and 24B can be eliminated. Fibers used to carry light tofilters and detectors in FIGS. 22B, 22C, 22B, 22C, and 24B can also beeliminated by using bulk optics. Alternatively, optical fibers can beused to guide the light. In some embodiments, the PBGF ends can besealed while gas can enter and exit the core of the PBGF through holesdrilled on the side of the fiber. In fact, many holes can be drilledalong the fiber to speed gas flow and make gas uniformly distributedalong the PBGF. In certain embodiments, however, gas enters and/or exitsthe PBGF through one or both endfaces.

Other variations are also possible. Additional components can be addedto the systems. Likewise, some components in FIGS. 22, 23, and 24 can beomitted and/or locations changed in different embodiments. Otherconfigurations and variations are also possible. The components can alsobe designed differently. For example, other configurations and designsthe multiplexers and demultiplexers may be used. In certain embodiments,one or both the multiplexer or demultiplexer may be excluded.Additionally, in any of the example applications described herein asingle continuous PBGF or separate portions of PBGF may be used.

EXAMPLES

Any two dielectric media with different refractive indexes can be usedto implement the fiber structures described herein. A suitable candidatefor the high index material is glass, especially fused silica glasswhich is advantageous physical and optical properties, and durability.The low index medium can be chosen from one or a mixture of gases orvacuum. This choice of low index material has high nonlinear threshold,low scattering and absorption loss, and very low dispersion.

A PBGF with a wide transmission band has many applications, e.g.telecommunication and trace gas analysis based on spectral absorption orRaman scattering techniques. Such a broad transmission band can beachieved in Bragg fibers with ν<π, i.e. d<0.5λ/(n_(h) ²−n₁ ²)^(1/2) andR<0.3. Wavelength scaling enables fiber designs for any wavelengthrange. The fiber dimension can be scaled proportionally to wavelength,i.e. double wavelength results in double fiber dimension.

Broad transmission band can also be achieved by reducing the averagethickness, d, in any cladding design which resembles a layered claddingstructure around a core. In certain embodiments comprising atriangularly stacked structure where reduced average d is used toachieve a 200 nm transmission band, ν<π and R<0.05. In the circularlystacked structure described in FIG. 4, for example, a 200 nmtransmission band can be achieved with ν<π, i.e. d<0.5λ/(n_(h) ²−n₁²)^(1/2) and R<0.2.

Low transmission loss is also advantageous for a range of applications.Loss can be reduced or minimized by operating at ν_(opt) determined byequation 7. In certain embodiments, the average thickness, d may be usedto estimate ν_(opt), in case where d varies circumferentially. Forexample, for R=0.2, ν_(opt)≈0.7π for m=1, 1.60π for m=2, and 2.56π form=3. For R=0.1, ν_(opt)≈0.67π for m=1, 1.58π for m=2, and 2.55π for m=3.

Low dispersion is also useful for telecommunications. In certainembodiments, core radius can be chosen to be larger than 10 μm toachieve dispersion below 20 ps/nm/km. In addition, the first layerthickness, δ, and refractive indices can be varied to tailor dispersion.The first layer thickness δ can be adjusted from 1% to 50% of d. In someembodiments, for example, δ (n_(h) ²−n₁ ²)^(1/2)/λ=0.01 to 2 can be usedto tailor dispersion. A large d can be used to achieve strong negativedispersion. For robust single mode operation, core radius ρ may besmaller than 15 μm in certain embodiments.

It may be useful for broad band transmission band to eliminate surfacemodes on the core/cladding boundary. In various embodiments, the δ(n_(h)²−n₁ ²)^(1/2)/λ of the core/cladding boundary may be less than about0.15 for a complete elimination of surface modes. The reduction of thefirst layer thickness will decrease confinement and increase modepenetration into the first layer, which leads to higher confinement lossand scattering loss from the first layer. In practice, a compromisebetween surface mode loss and confinement/scattering loss has to besought.

Other embodiments having different designs and configurations arepossible and should not be limited to those described above. Moreover,the above description of the preferred embodiments has been given by wayof example. From the disclosure given, those skilled in the art will notonly understand the present invention and its attendant advantages, butwill also find apparent various changes and modifications to thestructures and methods disclosed. It is sought, therefore, to cover allsuch changes and modifications as fall within the scope of theinvention, as defined by the appended claims, and equivalents thereof

1. A method of manufacturing a photonic bandgap fiber, said methodcomprising: arranging a plurality of tubes so as to form a plurality ofrings of tubes disposed about a center; excluding at least three ringsof tubes from said center to provide an open region; and stretching saidplurality of tubes thereby reducing the size of said rings and said openregion so as to form a photonic bandgap fiber comprising a core and acladding disposed about said core, wherein said cladding includes afirst plurality of ring shaped regions comprising a high refractiveindex material and a second plurality of ring shaped regions comprisinga low refractive index material, wherein said first plurality of ringshaped regions has an average thickness, d, and an average periodicity,Λ, and said average thickness, d, of said high index material is limitedsuch that the ratio d/Λ is less than approximately 0.2, and wherein saidexcluding and stretching affect an optical characteristic of saidphotonic bandgap fiber at a design wavelength.
 2. The method of claim 1,wherein tubes are arranged in a triangular pattern and said rings arehexagonal.
 3. The method of claim 1, wherein excluding said at leastthree rings comprise removing at least three rings of tubes from saidcenter.
 4. The method of claim 1, wherein at least four rings of tubesare excluded from said center.
 5. The method of claim 1, wherein atleast five rings of tubes are excluded from said center.
 6. The methodof claim 1, wherein said tubes are stretched such that the size of saidopen region is substantially equal to a predetermined core size.
 7. Themethod of claim 1, wherein said tubes are stretched such that the widthof said open region is between about 10 to 15 μm.
 8. The method of claim1, wherein the plurality of tubes are arranged in a circular pattern. 9.The method of claim 1, wherein the first plurality of ring shapedregions circular.
 10. The method of claim 9, wherein the first pluralityof ring shaped regions are concentric.
 11. The method of claim 1,wherein the first plurality of ring shaped regions and the secondplurality of ring shaped regions alternate.
 12. The method of claim 1,wherein said optical characteristic comprises at least one oftransmission bandwidth, transmission loss and dispersion.
 13. The methodof claim 1, wherein the average thickness, d, of the high index materialis limited such that the ratio d/Λ A is less than approximately 0.1. 14.The method of claim 2, wherein at least nineteen rings are excluded fromsaid hexagonal pattern such that the transmission bandwidth of saidphotonic bandgap fiber is greater than approximately 100 nm.